My research interests primarily lie in the analysis of partial differential equations, mathematical finance, and mean field theory.
Specifically, I focus on the mathematics of liquid crystals, portfolio selection in financial markets, and mean field game/control problems.
Publications/ Preprints:
(11). Landau-de Gennes energy with weak planar anchoring
with Yong Yu,
submitted, preprint available here (2026).
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(10). Optimal matching strategies in two-sided markets: A mean field approach
with Erhan Bayraktar, Dantong Chu and Bohan Li,
submitted, preprint available here (2025).
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(9). Viscosity solutions of fully second-order HJB equations in the Wasserstein space,
with Erhan Bayraktar, Hang Cheung, Ibrahim Ekren, Jinniao Qiu and Xin Zhang,
to appear in SIAM Journal on Control and Optimization, preprint available here (2026).
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(8). A variational approach to portfolio choice,
with Paolo Guasoni and Emmet Lawless,
submitted, preprint available here (2025).
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(7). Incentives of defined-contribution pension managers,
with Paolo Guasoni, Bohan Li, Tak Kwong Wong and Sheung Chi Phillip Yam,
submitted (2024).
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(6). A control theoretical approach to mean field games. Part II: global well-posedness of master equations, [Article]
with Alain Bensoussan, Tak Kwong Wong and Sheung Chi Phillip Yam,
Applied Mathematics and Optimization 93(45) (2026).
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(5). A control theoretical approach to mean field games. Part I: global equilibrium solution, [Article]
with Alain Bensoussan, Tak Kwong Wong and Sheung Chi Phillip Yam,
Applied Mathematics and Optimization 92(44) (2025).
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(4). Mean field type control problems, some Hilbert-space-valued FBSDEs, and related equations, [Article]
with Alain Bensoussan and Sheung Chi Phillip Yam,
ESAIM: Control, Optimisation and Calculus of Variations 31:33 (2025).
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(3). Viscosity solutions of a class of second order Hamilton-Jacobi-Bellman equations in the Wasserstein space, [Article]
with Hang Cheung and Jinniao Qiu,
Applied Mathematics and Optimization 91(23) (2025).
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(2). Pattern formation in Landau-de Gennes theory, [Article]
with Yong Yu,
Journal of Functional Analysis 285(1), 109923 (2023).
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(1). Singular solutions to some semilinear elliptic equations: an approach of Born-Infeld approximation, [Article]
with Chia-Yu Hsieh and Yong Yu,
Communications in Mathematical Sciences 19(2), 557–584 (2021).